A tearsheet is what you call a magazine ad or editorial or ad camapign or catalog that you have done, and you rip it out of the magazine and put it in your modeling portfolio. So see, yes the portfolio is needed.
Yes the web means that you can have your photo on the agency website, but that doesn't mean you don't need marketing tools and a portfolio!
I bring my portfolio to all my castings.
I bring my compcard too.
Some agencies scam girls by making them pay to get a modeling portfolio shot, and a compcard created.
But honestly, if you take it upon yourself and you think like a business, you can make your own compcard and modeling portfolio photos. Don't wait! Invest in yourself.
You really need to work with good photographers. And modeling doesn't have to be sexy! What about modeling for hair, beauty, shoes, jewerly, handbags, ect??? But to get work doing this, it would be best to show yourself modeling these items in your shots, and looking at ads and editorials and creating the shots you need.
It is easy to start yourself but you need to work with good photographers, and do your research, and be involved with your pursuits.
Set goals for yourself. You can freelance with an agency but that doesn't mean you can't find your own modeling work too. If you live in a small town, why not drop by a local hair salon and ask if they might need a model for their window ads?
Bring your portfolio, and compcard.
Having a tearsheet can help you get interest from an agent. It's like having experience before you go for the job.